Abstract
The notion of a τ-exceptional sequence was introduced by Buan and Marsh in (2018) as a generalisation of an exceptional sequence for finite dimensional algebras. We calculate the number of complete τ-exceptional sequences over certain classes of Nakayama algebras. In some cases, we obtain closed formulas which also count other well known combinatorial objects, and exceptional sequences of path algebras of Dynkin quivers.
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Presented by: Henning Krause
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This research was supported by an EPSRC Doctoral Training Partnership (reference EP/R513258/1) through the University of Leeds. The author also wishes to thank their supervisor, Bethany Marsh for their support. Lastly, but not least, the author also thanks the referees of this paper for their comments on an earlier version of the paper.
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Msapato, D. Counting the Number of τ-Exceptional Sequences over Nakayama Algebras. Algebr Represent Theor 25, 1071–1105 (2022). https://doi.org/10.1007/s10468-021-10060-y
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DOI: https://doi.org/10.1007/s10468-021-10060-y
Keywords
- τ-Exceptional sequence
- Exceptional sequence
- Nakayama algebras
- τ-Perpendicular category
- Restricted Fubini numbers